## GroupSound

Underlying many digital signal processing (dsp) algorithms, in particular those used for digital audio filters, is the convolution operation, which is a weighted sum of translations $f(x-y)$. Most classical results of dsp are easily and elegantly derived if we define our functions on $\mathbb{Z}/n\mathbb{Z}$, the abelian group of integers modulo n. If we replace this underlying "index set" with a nonabelian group, then translation may be written $f(y^{-1}x)$, and the resulting audio filters arising from convolution naturally produce different effects than those obtained with ordinary (abelian group) convolution.